This questions debates the SEO value between the following two options:
Having your forum located in a folder, found in the URL slug, such as domain.com/forum.
Having your forum located in a sub-domain like forum.domain.com.
This question usually comes up because of the desire to ensure that all your inbound links are juicing the entire website, not just a part of it.
In our opinion, there's no difference if the forum is in a folder or sub-domain. If the content on a sub-domain is on a different web-server and IP address, it’s a good idea to register the sub-domain in your Google Webmaster Tools account. This way, Google knows that the website and forum are one and the same and you’ll get SEO juice for inbound links to the forum.